This tutorial illustrates the core visualization utilities available in Ax.
import numpy as np
from ax.service.ax_client import AxClient
from ax.modelbridge.cross_validation import cross_validate
from ax.plot.contour import interact_contour
from ax.plot.diagnostic import interact_cross_validation
from ax.plot.scatter import(
interact_fitted,
plot_objective_vs_constraints,
tile_fitted,
)
from ax.plot.slice import plot_slice
from ax.utils.measurement.synthetic_functions import hartmann6
from ax.utils.notebook.plotting import render, init_notebook_plotting
init_notebook_plotting()
[INFO 11-15 16:59:07] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.
The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials
noise_sd = 0.1
param_names = [f"x{i+1}" for i in range(6)] # x1, x2, ..., x6
def noisy_hartmann_evaluation_function(parameterization):
x = np.array([parameterization.get(p_name) for p_name in param_names])
noise1, noise2 = np.random.normal(0, noise_sd, 2)
return {
"hartmann6": (hartmann6(x) + noise1, noise_sd),
"l2norm": (np.sqrt((x ** 2).sum()) + noise2, noise_sd)
}
ax_client = AxClient()
ax_client.create_experiment(
name="test_visualizations",
parameters=[
{
"name": p_name,
"type": "range",
"bounds": [0.0, 1.0],
}
for p_name in param_names
],
objective_name="hartmann6",
minimize=True,
outcome_constraints=["l2norm <= 1.25"]
)
[INFO 11-15 16:59:07] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 11-15 16:59:07] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).
[INFO 11-15 16:59:07] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.
[INFO 11-15 16:59:07] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.
for i in range(20):
parameters, trial_index = ax_client.get_next_trial()
# Local evaluation here can be replaced with deployment to external system.
ax_client.complete_trial(trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters))
/home/runner/work/Ax/Ax/ax/core/observation.py:274: FutureWarning:
In a future version of pandas, a length 1 tuple will be returned when iterating over a groupby with a grouper equal to a list of length 1. Don't supply a list with a single grouper to avoid this warning.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.520778, 'x2': 0.896136, 'x3': 0.844505, 'x4': 0.873872, 'x5': 0.773733, 'x6': 0.149381}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.66481, 0.1), 'l2norm': (1.695921, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.208775, 'x2': 0.315463, 'x3': 0.920839, 'x4': 0.781654, 'x5': 0.445667, 'x6': 0.735724}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.433322, 0.1), 'l2norm': (1.344793, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.675836, 'x2': 0.53783, 'x3': 0.317482, 'x4': 0.869316, 'x5': 0.142102, 'x6': 0.980962}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.053448, 0.1), 'l2norm': (1.470961, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.010167, 'x2': 0.206961, 'x3': 0.105612, 'x4': 0.13704, 'x5': 0.833047, 'x6': 0.334161}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.001015, 0.1), 'l2norm': (0.954551, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.769783, 'x2': 0.458056, 'x3': 0.600782, 'x4': 0.521409, 'x5': 0.707924, 'x6': 0.105385}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.131503, 0.1), 'l2norm': (1.409098, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.816021, 'x2': 0.286038, 'x3': 0.221903, 'x4': 0.868841, 'x5': 0.993434, 'x6': 0.125464}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (0.171501, 0.1), 'l2norm': (1.617744, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.579393, 'x2': 0.108716, 'x3': 0.654682, 'x4': 0.859262, 'x5': 0.503269, 'x6': 0.485744}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.080537, 0.1), 'l2norm': (1.333622, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.053399, 'x2': 0.518407, 'x3': 0.63117, 'x4': 0.292651, 'x5': 0.117334, 'x6': 0.513588}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.636254, 0.1), 'l2norm': (0.970186, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.807286, 'x2': 0.426385, 'x3': 0.993155, 'x4': 0.46455, 'x5': 0.04808, 'x6': 0.417423}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.154915, 0.1), 'l2norm': (1.59603, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.503278, 'x2': 0.456377, 'x3': 0.715134, 'x4': 0.820531, 'x5': 0.422812, 'x6': 0.449279}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (0.158567, 0.1), 'l2norm': (1.47523, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.314738, 'x2': 0.243882, 'x3': 0.898765, 'x4': 0.994575, 'x5': 0.462922, 'x6': 0.638295}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.069739, 0.1), 'l2norm': (1.636, 0.1)}.
[INFO 11-15 16:59:07] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.393801, 'x2': 0.225783, 'x3': 0.703269, 'x4': 0.80026, 'x5': 0.267139, 'x6': 0.196064}.
[INFO 11-15 16:59:07] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.043225, 0.1), 'l2norm': (1.309466, 0.1)}.
[INFO 11-15 16:59:15] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.029918, 'x2': 0.4568, 'x3': 0.742434, 'x4': 0.379994, 'x5': 0.201568, 'x6': 0.613351}.
[INFO 11-15 16:59:15] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.406885, 0.1), 'l2norm': (1.188848, 0.1)}.
[INFO 11-15 16:59:34] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.015176, 'x2': 0.428097, 'x3': 0.785965, 'x4': 0.289183, 'x5': 0.255104, 'x6': 0.640736}.
[INFO 11-15 16:59:34] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.678846, 0.1), 'l2norm': (1.102621, 0.1)}.
[INFO 11-15 16:59:46] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.0, 'x2': 0.441888, 'x3': 0.849021, 'x4': 0.232976, 'x5': 0.239591, 'x6': 0.668874}.
[INFO 11-15 16:59:46] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.263377, 0.1), 'l2norm': (1.168782, 0.1)}.
[INFO 11-15 16:59:59] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.0, 'x2': 0.379795, 'x3': 0.761359, 'x4': 0.302417, 'x5': 0.329868, 'x6': 0.635639}.
[INFO 11-15 16:59:59] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.814461, 0.1), 'l2norm': (0.964942, 0.1)}.
[INFO 11-15 17:00:08] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.000648, 'x2': 0.362727, 'x3': 0.75432, 'x4': 0.341839, 'x5': 0.337304, 'x6': 0.721589}.
[INFO 11-15 17:00:08] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.813246, 0.1), 'l2norm': (1.344924, 0.1)}.
[INFO 11-15 17:00:23] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.0, 'x2': 0.297202, 'x3': 0.77097, 'x4': 0.341895, 'x5': 0.315669, 'x6': 0.633067}.
[INFO 11-15 17:00:23] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.917988, 0.1), 'l2norm': (1.142149, 0.1)}.
[INFO 11-15 17:00:32] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.0, 'x2': 0.351537, 'x3': 0.792547, 'x4': 0.380941, 'x5': 0.367298, 'x6': 0.607249}.
[INFO 11-15 17:00:32] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-1.564152, 0.1), 'l2norm': (1.258171, 0.1)}.
[INFO 11-15 17:00:40] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.0, 'x2': 0.274521, 'x3': 0.72327, 'x4': 0.304967, 'x5': 0.298579, 'x6': 0.66905}.
[INFO 11-15 17:00:40] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.11401, 0.1), 'l2norm': (1.066039, 0.1)}.
The plot below shows the response surface for hartmann6 metric as a function of the x1, x2 parameters.
The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them.
# this could alternately be done with `ax.plot.contour.plot_contour`
render(ax_client.get_contour_plot(param_x="x1", param_y="x2", metric_name='hartmann6'))
[INFO 11-15 17:00:40] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.
The plot below allows toggling between different pairs of parameters to view the contours.
model = ax_client.generation_strategy.model
render(interact_contour(model=model, metric_name='hartmann6'))
This plot illustrates the tradeoffs achievable for 2 different metrics. The plot takes the x-axis metric as input (usually the objective) and allows toggling among all other metrics for the y-axis.
This is useful to get a sense of the pareto frontier (i.e. what is the best objective value achievable for different bounds on the constraint)
render(plot_objective_vs_constraints(model, 'hartmann6', rel=False))
CV plots are useful to check how well the model predictions calibrate against the actual measurements. If all points are close to the dashed line, then the model is a good predictor of the real data.
cv_results = cross_validate(model)
render(interact_cross_validation(cv_results))
Slice plots show the metric outcome as a function of one parameter while fixing the others. They serve a similar function as contour plots.
render(plot_slice(model, "x2", "hartmann6"))
Tile plots are useful for viewing the effect of each arm.
render(interact_fitted(model, rel=False))
Total runtime of script: 1 minutes, 52.73 seconds.